The holiday shopping season is the most important time of year for retailers. And with the holidays just around the corner, it's time for investors to fill their shopping carts with their favorite retail stocks. However, Abercrombie & Fitch (NYSE:ANF) and Gap Inc. (NYSE:GPS) are two retailers that investors may want to avoid. Without a strong e-commerce presence, these brick-and-mortar retailers could face holiday headwinds during the critical months ahead.

Troubled waters for mall-based stores
Teen retail chain Abercrombie & Fitch and apparel giant Gap pander to different demographics of shoppers, but both companies are primarily mall-based retailers. They are therefore especially vulnerable to online rivals such as Amazon.com (NASDAQ:AMZN). Their respective stocks have something in common as well: Both stocks are down double digits year to date. Shares of Gap have plummeted more than 34% so far this year, followed by a 24% decline in shares of Abercrombie over the same period.

And both stocks could have further to fall if the companies can't capture meaningful sales gains during the holidays. Retail chains such as Abercrombie and Gap, after all, rely on the November and December months for as much as 30% of their total annual income.

This year, online channels will play an increasingly important role in driving sales for brick-and-mortar retailers. "Digital interactions will influence 64%, or $434 billion, of retail store sales this holiday season," according to a study by Deloitte. Without a focused e-tail strategy, Abercrombie and Gap could fall behind its rivals in the space.

Walk the walk or perish
Abercrombie has paid a lot of lip service to developing a strong mobile and digital platform, but the teen retailer has a way to go before its digital channel will help offset the significant slowdown in mall traffic. True, the company's online sales -- direct-to-consumer -- have inched higher over the years, climbing from just 7% of total sales in 2008 to roughly 23% of total net sales in its fiscal 2015 first quarter.

However, the retailer was late to the mobile game. Abercrombie & Fitch didn't launch a mobile site or smartphone application until 2010. By that time, tens of thousands of third-party sellers were already hawking A&F-branded gear on Amazon's site. Moreover, it wasn't until this year that Abercrombie's leadership said it would make a concerted effort to transition from a "brand-led" company to a "mobile-led" business.

Source: The Motley Fool.

Getting it right on the mobile front is particularly important for Abercrombie & Fitch because it caters to tech-savvy teens. A&F has lost its popularity among teens recently. The company reported a loss of $0.01 per share for its fiscal second quarter, down from a year-ago profit of $0.17 per share.

Abercrombie has multiple factors working against it heading into the holidays. Not only does the convenience of online shopping continue to erode mall traffic, but also the teen-retail segment has been hit the hardest. Mall-based teen-retail outlets Wet Seal and dELiA*s recently declared bankruptcy, and American Apparel and Aeropostale are perhaps not far behind.

Source: The Motley Fool.

With more than 3,300 mall-based stores worldwide, Gap faces a similar challenge. A record number of consumers are expected to shop online this holiday season. In fact, FedEx (NYSE:FDX) estimates that its U.S. shipments will increase an astounding 12% from Black Friday through Christmas Eve this year. The shipping and logistics company plans to add upwards of 55,000 seasonal employees to help keep up with this spike in holiday volume.

Similar to other mall-based retailers, Gap is in the process of transitioning to a more digital-centric business model. This process is proving easier said than done. The apparel retailer posted a 2.1% decline in online sales for its fiscal 2015 first quarter, with e-commerce sales coming in at $563 million, down from $575 million a year ago.

Gap plans to close as many as 175 of its mall stores over the next two years in an attempt to better focus resources on its e-commerce ambitions. The option to reserve online and pick up in the store that Gap rolled out last year has helped integrate its mobile and physical customer experiences. However, it will take more than in store pick-ups to reinvigorate traffic at its brick-and-mortar locations.

On top of this challenge, Gap can't seem to get the e-commerce thing right. The company dumped its only full-scale online outfit, known as Piperlime, earlier this year. Piperlime sold higher-end shoes and clothing and was meant to compete with Amazon's Zappos.com business. In a press release, Gap said the decision "allows the company to remain focused on its top priorities." I guess dominating the e-commerce scene is no longer a top priority.

Malls are so last season
The brick-and-mortar stores that are winning today have seamlessly integrated mobile and e-commerce platforms and a clear understanding of how their customers use social media to connect with their favorite brands. Both Abercrombie and Gap are making the necessary strides to get their respective digital strategies up to speed today. However, their digital reputations are not yet strong enough to counterbalance the fallout at mall-based stores.

Investors are better off putting their money behind e-commerce giant Amazon or even logistics companies such as FedEx ahead of the holiday season, because of the increasing popularity in online shopping.

Tamara Rutter owns shares of Amazon.com. The Motley Fool owns shares of and recommends Amazon.com. The Motley Fool recommends FedEx. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.